E.M.F. Equation of an Alternator : Part2 In practice short pitch coils are preferred. So coil is form by connecting one coil side to another which is less than one pole pitch away. So actual span is less than 180o. The coil is generally shorted by one or two slots.Note: The angle by which coil are short pitched is called angle or short pitched is called angle of short pitch denoted as ''.= Angle by which coils are short pitched. As coils are shorted in terms of number of slots i.e. either by one slot, two slots and so on and slot angle is then angle of short pitch is always a multiple of the slot angle .

Fig. 1 Angle for short pitch

... = x Number of slots by which coils are short pitched. or = 180o-Actual coil span of the coils. This is shown in the Fig. 1. Now let E be the induced e.m.f. in each coil side. If coil is full pitch coil, the induced e.m.f. in each coil side help each other. Coil connections are such that both will try to set up a current in the same direction in the external circuit. Hence the resultant e.m.f. across a coil will be algebraic sum of the two....ER = E + E = 2E .......... for full pitch

Fig. 2 Full pitch coil

Now the coil is short pitched by angle '', the two e.m.f. in two coil sides no longer remains in phase from external circuit point of view. Hence the resultant e.m.f. is also no longer remains algebraic sum of the two but becomes a phasor sum of the two as shown in the Fig. 3.

Fig. 3 Phasor sum of two e.m.f.s

Obviously ERin such a case will be less than what it is in case of full pitch coil. From the geometry of the Fig. 3, we can write, AC is perpendicular drawn on OB bisecting OB.

... l(OC) =l(CB) = ER/2and

BOA =/2...cos (/2) = OC/OA = ER/2E...ER= 2 E cos (/2) ............... For short pitch This is the resultant e.m.f. in case of a short pitch coil which depends on the angle of short pitch ''.Note: Now the factor by which, induced e.m.f. gets reduced due to short pitching is called pitch factor or coil span factor denoted by Kc. It is defined as the ratio of resultant e.m.f. when coil is short pitch to the resultant e.m.f. when coil is full pitched. It is always less than one.

where = Angle of short pitch Related Articles :-E.M.F. Equation of an Alternator

E.M.F. Equation of an Alternator : Part3 Similar to full pitch coils, concentrated winding is also rare in practice. Attempt is made to use all the slots available under a pole for the winding which makes the nature of the induced e.m.f. more sinusoidal. Such a winding is called distributed winding.Consider 18 slots, 2 pole alternator. So slots per pole i.e. n = 9. m = Slots per pole per phase = 3 = 180o/9 = 20o Let E = Induced e.m.f. per coil and there are 3 coils per phase. In concentrated type all the coil sides will be placed in one slot under a pole. So induced e.m.f. in all the coils will achieve maxima and minima at the same time i.e. all of them will be in phase. Hence resultant e.m.f. after connecting coils in series will be algebraic sum of all the e.m.f.s. as all are in phase. As against this, in distributed type, coil sides will be distributed, one each in the 3 slots per phase available under a pole as shown in the Fig. 1(a).

Fig. 1

Thought the magnitude of e.m.f. in each coil will be same as 'E', as each slot contributes phase difference of oi.e. 20oin this case, there will exist a phase difference of owith respect to each other as shown in the Fig. 1(b). Hence resultant e.m.f. will be phasor sum of all of them as shown in the the Fig. 2. So due to distributed winding resultant e.m.f. decreases.

Fig. 2 Phasor sum of e.m.f.s

Note: The factor by which there is a reduction in the e.m.f. due to distribution of coils is called distribution factor denoted as Kd. Let us see the derivation for its expression. In general let there be 'n' slots per pole and 'm' slots per pole per phase. So there will be 'm' coils distributed under a pole per phase, connected in series. Let E be the induced e.m.f. per coil. Then all the 'm' e.m.f.s induced in the coils will have successive phase angle difference of = 180o/n. While finding out the phasor sum of all of them, phasor diagram will approach a shape of a 'm' equal sided polygon circumscribed by a semicircle of radius 'R'. This is shown in the Fig. 3. AB, BC, CD etc, represents e.m.f. per coil. All the ends joined at 'O' which is center of the circumscribing semicircle of raduis 'R'.

Fig. 3 Phasor sum of 'm' e.m.f.s

Angle subtended by each phasor at the origin 'O' is o. This can be proved as below. All the triangles OAB, OBC .... are similar and isosceles, as AB = BC = CD = ... = E. OAB = OBA = OBC = .... = x AOB = BOC = ... = y say Now in OAB, 2x + y = 180 while OBA + OBC + = 180o ................. (3) i.e. 2x + = 180o Comparing (3) and (4), y = So AOB = BOC = COD = ... = If 'M' is the last point of the last phasor, AOM = m x = m and AM = ER= Resultant of all the e.m.f.s. Consider a OAB separately as shown in the Fig. 4. Let OF be the perpendicular drawn on AB bisecting angle at apex 'O' as /2.

Fig. 4

l(AB) = E ... l(AF) = E/2 andl(OA) = R....sin (/2) = AF/OA = (E/2)/R...E = 2R sin (/2) ........... (5) Now consider OAM as shown in the Fig. . 3 and OG is the perpendicular drawn from 'O' on its base bisecting OAM....AOG = GOM = (m)/2... l(AM) = E...l(AG) = E/2 = 2 (OA) sin (m/2) Arithmetic sum of e.m.f.s = Arc AB = OA x (m)

Note: The angle (m/2) in the denominator must be in radians.Note: The above formula is used to calculate distribution factor when phase spread is and the winding is uniformly distributed.